An application of the variational analysis to calculate the meson spectral functions

TL;DR

This paper introduces a variational method to compute meson spectral functions on the lattice, enabling extraction of discrete spectral features and analysis of meson states at various temperatures.

Contribution

The paper presents a novel variational approach for calculating meson spectral functions on the lattice, improving accuracy and enabling analysis of excited states and temperature effects.

Findings

Method accurately reproduces free quark spectral functions.

Ground state charmonium peaks match conventional methods.

Potential survival of J/ψ and η_c up to 1.4 T_c.

Abstract

We present a new method to calculate meson spectral functions (SPFs) on the lattice based on a variational method. Because, on a finite volume lattice, the meson SPFs have discrete spectra only, a suitable way to extract such discrete signals is needed. Using a variational method, we can calculate several discrete quantities such as the position and the area of spectral peaks for low-lying states. Moreover data accuracy can be improved by increasing the number of basis functions. In this report, we first confirm our method in the free quark case and show that our method works well. Then, we apply the method to a quenched lattice QCD simulation and calculate the charmonium SPFs for S and P-waves at zero temperature. Our results for the ground state are well consistent with the position and the area of the lowest peaks of charmonium SPFs calculated by the conventional maximum entropy method. For first excited states, the signals may be reliablly extracted with our method because the charmonium mass converges to a value close to the experimental one when the number of basis functions is increased. We also investigate the SPFs for S-wave charmonia at below and above $T_c$. Our results suggest that $J/\psi$ and $\eta_c$ may survive up to 1.4$T_c$.